Dynamic Bayesian Networks Cora Perez-Ariza 1 , Ann Nicholson 2 , - - PowerPoint PPT Presentation

Causal Discovery of Dynamic Bayesian Networks

Cora Perez-Ariza1, Ann Nicholson2, Kevin Korb2, Steven Mascaro2 and Chao Heng Hu2

1

• Dept. of Computer Science and Artificial Intelligence

University of Granada

2

Clayton School of IT Monash University

Learning Static BNs

Constraint-based learning

 Performs independence tests  e.g. PC algorithm (Spirtes et al., 1993)  Tests all pairs for direct dependencies

Learning Static BNs

Constraint-based learning

 Performs independence tests  e.g. PC algorithm (Spirtes et al., 1993)  Tests all pairs for direct dependencies Finding a graph pattern Finding head to head arcs and orient the rest

Learning Static BNs

Metric-based learning

 (Stochastic) search and score  Learning programs/packages: e.g. CaMML (Causal discovery via

MML), BNT (Bayes Net Toolbox).

Learning Static BNs

Metric-based learning

 (Stochastic) search and score  Learning programs/packages: e.g. CaMML (Causal discovery via

MML), BNT (Bayes Net Toolbox).

Score and rank M → M' : Add/remove/reverse arcs add remove reverse

t2

Dynamic Bayesian Networks

Extension of BN with arcs from t → t + 1 DBNs that we consider:

• 1. Same structure for each slice (i.e. stationary)
• 2. Arcs cannot span more than one time step

t0 t1

Learning Dynamic Bayesian Networks

Why not use existing static learners?



Need to guarantee slice t nodes come before slice t+1 nodes



Often want slices to be the same (i.e. stationary)



Make the search more efficient  Produce better models

Learning DBNs – Previous Approaches

Friedman et al. (1998)

 Uses BIC/BDe scoring

 Hill-climbing  Learn the prior/initial network and the transition network

Prior network Transition network

+

The corresponding DBN

Learning DBNs – Previous Approaches

Bayes Net Toolbox (BNT)

 Written by Kevin Murphy (2001)  Supports DBN learning and inference

BNT algorithm

 Uses BIC/ML scoring  Guarantees that  Only learns arcs between slices (temporal arcs)

Two New Approaches to Learning DBNs

• 1. Enforce stationary DBN structure with structural

priors

• 2. Enhance existing search and score procedure to

take DBN structure into account

Both take advantage of our BN learner software CaMML

CaMML



Bayesian network learner created at Monash



Uses MML for score and MCMC for search



Can specify flexible priors:

• A -> B: Direct causal connection
• A – B: Direct relation
• A => B: Ancestral relation
• A ~ B: Correlation
• Tiers
• Existing BN structure

CaMML



Bayesian network learner created at Monash



Uses MML for score and MCMC for search



Can specify flexible priors:

• A -> B: Direct causal connection
• A – B: Direct relation
• A => B: Ancestral relation
• A ~ B: Correlation
• Tiers
• Existing BN structure

CaMML Tier Priors Learning

CaMML Tier Priors Learning

t2 t0 t1

Motivation, SES, Education ≺ Motivation1, SES1, Education1

≺

CaMML 2-Step Learning

Learn transitional arcs t0 Data BN for t0 Learn from Data Learned DBN Copy Network t0 t1

Experiments

Test models

We compare CaMML against two other learning programs:

• PC algorithm (in GeNIe)
• BNT

Milk Infection DBN

Mutual information Use mutual information to score strength of arcs

t0 t1

BAT DBN

Too many variables to show!

t0 t1



Plain static BN learning (without using priors)



CaMML vs GeNIe (PC algorithm)

Experiment #1



Learning with tier priors



CaMML vs GeNIe and BNT

Experiment #3 Experiment #2



Learning using tier priors vs 2-step algorithm

Experiment Procedure

Known Models Tier or BN Priors Learned Models Generate Data Learn DBNs Test with ED/CKL

Evaluation

Edit distance

Count 1 if an arc is missing/added/reversed in the learned model Our modification for DBNs: EDDBN = Ws.Ns + Wt.Nt

Causal Kullback-Leibler divergence

Computes the distance of probability distribution between model P and model Q

Milk and cancer model (CaMML vs GeNIe, using tiers)

Results

Milk and cancer model (CaMML vs GeNIe, using tiers)

Results

Results

Transitional arc errors for the BAT network

Datasize CaMML w/ Tiers GeNIe (PC) BNT 500 6.8 (0.98) 13 7.5 (0.50) 5000 5.4 (1.62) 10 6.2 (0.74) 50000 1.0 (0.0) 10 3.7 (0.33)

5 10 15 20 25 30 35 total errors (tiers) total errors (Alg)

Results

BAT model (CaMML, tiers vs 2-step learning)

500 5000 50000 Data size Errors

5 10 15 20 25 static errors (tiers) static errors (Alg)

BAT model (CaMML, tiers vs 2-step learning)

Errors

Results

500 5000 50000 Data size

2 4 6 8 10 12 14 temporal errors (tiers) temporal errors (Alg)

BAT model (CaMML, tiers vs 2-step learning)

500 5000 50000 Data size Errors

Results

Summary

GeNIe(PC) tends to over-fit (i.e. more arcs added) with large data size in Experiment #1. Using tiers, CaMML produces fewer errors than BNT and GeNIe(PC). CaMML can recover more weak arcs, and usually learns all the strong arcs. The 2-step learning algorithm produces comparable results, better at learning static arcs.

CaMML 2-Step Learning Issues

CaMML 2-Step Learning Issues

Current and Future Work

 Modify CaMML’s search and score:

• Alter score to avoid double counting static

arcs

• Alter search to avoid invalid DBN structures
• Ultimately: Reduce the search space so that

we can find good models more quickly